The exam topics
Mathematics for Economics
The mathematics of Economics degrees: functions and economic models, limits, derivatives and elasticity, optimization, integrals, financial mathematics, matrices and systems, functions of two variables.
Real functions and economic models
What a real function is, how to find its domain, graph, inverse and composition, how linear, quadratic, exponential and logarithmic functions behave, and how they describe demand, supply, costs, revenues and profits.
Sequences, progressions and series
How quantities that change at regular intervals are described by sequences, how the terms and sums of arithmetic and geometric progressions are computed, what it means for a sequence to have a limit, and when a sum of infinitely many terms gives a finite number.
Limits and continuity
What it means for a function to approach a value, how limits are computed and indeterminate forms resolved, how asymptotes are found, what a continuous function is and what the intermediate zero theorem and the Weierstrass theorem guarantee.
Derivatives, marginal functions and elasticity
What the derivative is and how to compute it with the differentiation rules, what marginal cost, marginal revenue, marginal profit and the elasticity of demand measure, and what Fermat's, Rolle's and Lagrange's theorems and de l'Hôpital's rule say.
Curve sketching and optimization
How to find and classify the maxima and minima of a function with the first derivative and the second derivative, how to study concavity and inflections, how to sketch the graph with the complete curve sketching scheme and how to solve optimization problems, including those on profit, average cost and revenue.
Integral calculus and economic applications
How to find the antiderivatives of a function with basic integrals, by substitution, by parts and with partial fractions, what the definite integral and the integral function are, what the mean value theorem and the fundamental theorem of calculus say, and how integrals are used to compute areas, total costs, surpluses and present values.
Compounding, annuities and amortization
How a capital grows under simple, compound and continuous compounding, how amounts are brought to the same date with present value and equivalent rates, how annuities and amortization schedules are valued, and how an investment is assessed with NPV and IRR.
Matrices, determinants and linear systems
How to work with matrices, how to compute the determinant, the inverse and the rank, when a linear system has solutions and how to find them with Cramer, Rouché-Capelli and Gauss, also in the presence of a parameter, with the equilibrium of two markets and the Leontief model.
Functions of two variables
How points and sets of the plane are described, how to find the domain and the level curves of a function of two variables, how to compute partial derivatives, the gradient, the tangent plane and the differential, and how they are used to study production, utility and returns to scale.
Unconstrained and constrained extrema
How to find and classify the maxima and minima of a function of two variables, with stationary points and the Hessian matrix, how to look for absolute extrema on a closed and bounded set and extrema on a constraint, with substitution and with Lagrange multipliers, and how these methods solve the problems of profit, of the consumer and of minimum cost.